发表机构
Beijing University of Technology; State Key Laboratory of Bridge Safety and Resilience（北京工业大学; 桥梁安全与韧性国家重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究强迫物理系统中潜在响应规律，提出FLARE方法，通过学习紧凑响应坐标等，能恢复强迫动力学并预测高维响应，还可将方程发现扩展到复杂观测系统，为可解释建模和预测提供途径。
AI 中文摘要
控制方程提供了物理系统的简洁描述，但其简单的变量常隐藏于高维测量中。对于强迫系统，这一挑战更为严峻，其响应依赖于内在动力学和随时间变化的输入。本文引入FLARE，一种用于响应方程的强迫潜在自动编码器，它能学习紧凑响应坐标，识别稀疏输入依赖的潜在动力学，并将方程展开解码为完整响应。通过从数据估计潜在维度并将状态估计与外部强迫分离，FLARE能根据过去响应初始化预测并由规定的未来输入驱动。在已知动力系统、应用规模的强迫响应和视觉观测中，FLARE能恢复紧凑的强迫动力学并预测未用于训练的输入下的长期高维响应。通过将学习到的坐标转化为动态界面，FLARE将方程发现扩展到有效状态隐藏在复杂观测中的系统，为强迫动力系统中高维响应的可解释建模和预测提供了途径。
英文摘要
Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements. This challenge is sharper for forced systems, whose responses depend on both intrinsic dynamics and time-dependent inputs. Here we introduce FLARE, a forced latent autoencoder for response equations that learns compact response coordinates, identifies sparse input-dependent latent dynamics and decodes equation rollouts to full responses. By estimating latent dimension from data and separating state estimation from external forcing, FLARE enables forecasts to be initialized from past responses and driven by prescribed future inputs. Across known dynamical systems, application-scale forced responses and visual observations, FLARE recovers compact forced dynamics and predicts long-horizon high-dimensional responses under inputs not used for training. By turning learned coordinates into a dynamical interface, FLARE extends equation discovery to systems whose effective states are hidden within complex observations, providing a route for interpretable modelling and prediction of high-dimensional responses in forced dynamical systems.
Comments23 pages, 5 figures and 2 tables. Supplementary Information provided as an ancillary file
